The C-program, equil2.c, which can be downloaded from this page predicts the concentrations of free ligand, receptor and ligand-receptor complex species from total ligand receptor concentrations. The equilibrium binding constants and the scheme of binding steps must be specified. An example input file is also provided.
Notes
The input file should contain i. a scheme of binding, ii. dissociation
constant of each binding step and iii. the concentrations of the total receptor
and ligand species. The concentration units are arbitrary but should be
consistent. In the mechanism part of the input file, each species is represented
by a one letter character with the free ligand and receptor represented by L
and R, respectively. The input file, scheme.txt, is a suitable example.
Upon executing the program, you will be prompted to provide the name of the input containing the relevant information. Then, you will be prompted for the name of an output file. This file will contain the calculated concentrations of the free ligand and receptor concentrations, as well as the total ligand and receptor concentrations. This option is included if you can not copy the data directly from the compiled program output (as I could not when running a Windows version of the program). A program session looks something like this:
Please type in the name of the input file
>scheme_nmr2a.txt
Equations for equilibrium binding:
L(tot) = L + B + C + 2D
R(tot) = R + B + 2A + 2C + 2D
B = L R / ( K0 )
A = R^2 / ( K1 )
C = L R^2 / ( K1 K2 )
D = L^2 R^2 / ( K1 K2 K3 )
K0 = 0.400000
K1 = 100000.000000
K2 = 0.000200
K3 = 0.026667
Outer - SPEC Inner - SPEC
| 75.000000 | 150.000000 | 0.059935724306927 | 63.062530612145821 |
| 150.000000 | 150.000000 | 2.772206422797975 | 2.138327169621676 |
| 300.000000 | 150.000000 | 150.051967664650050 | 0.039977172568126 |
| 525.000000 | 150.000000 | 375.020796552789190 | 0.015997675906782 |
| 750.000000 | 150.000000 | 600.012998822307400 | 0.009999222066006 |
| 1500.000000 | 150.000000 | 1350.005777576063100 | 0.004444314558930 |
As seen from the above example, the output consists of the equations which were solved to generate the data. Then, the concentrations of total ligand, total receptor, calculated free ligand and calculated free receptor are printed out. To calculate the concentrations of other species, I found it useful to copy and paste the data into a spreadsheet. Then, the concentrations of other species were calculated using the equations listed in the output. For example, the concentration of species B (one ligand bound to one receptor) is specified by B = L R / ( K0 ).
The Newton-Raphson method used to solve the set of non-linear equations is not perfect. In some cases, the method fails to converge on a solution. This is may be why Steve Chamberlin used a different method in this paper on simulating the EGF - EGF receptor system (Chamberlin and Davies, Biochim Biophys Acta. 1998. 1384(2):223-32.)
For any further queries about the program, please email me at robert.jorissen@ludwig.edu.au. I can provide a compiled executable version of the program for Windows PCs for interested people.